Evaluates the Student's t cumulative probability distribution function.

Namespace: Imsl.Stat
Assembly: ImslCS (in ImslCS.dll) Version: 6.5.0.0

Syntax

C#
public static double StudentsT(
	double t,
	double df
)
Visual Basic (Declaration)
Public Shared Function StudentsT ( _
	t As Double, _
	df As Double _
) As Double
Visual C++
public:
static double StudentsT(
	double t, 
	double df
)

Parameters

t
Type: System..::.Double
A double scalar value representing the argument at which the function is to be evaluated.
df
Type: System..::.Double
A double scalar value representing the number of degrees of freedom. This must be at least one.

Return Value

A double scalar value representing the probability that a Student's t random variable takes a value less than or equal to t.

Remarks

Method Cdf.StudentsT evaluates the distribution function of a Student's t random variable with df degrees of freedom. If the square of t is greater than or equal to df, the relationship of a t to an f random variable (and subsequently, to a beta random variable) is exploited, and routine Cdf.Beta is used. Otherwise, the method described by Hill (1970) is used. If df is not an integer, if df is greater than 19, or if df is greater than 200, a Cornish-Fisher expansion is used to evaluate the distribution function. If df is less than 20 and \left|{\rm t} \right| is less than 2.0, a trigonometric series (see Abramowitz and Stegun 1964, equations 26.7.3 and 26.7.4, with some rearrangement) is used. For the remaining cases, a series given by Hill (1970) that converges well for large values of t is used.

For greater right tail accuracy, see Cdf.ComplementaryStudentsT.

Student's t Distribution Function

See Also